\frac{dx_{1}}{dt} = \left(-1 \cdot k_{18} \cdot k_{4} \cdot x_{4} \cdot x_{1} + -1 \cdot k_{18} \cdot k_{2} \cdot \left(1 - x_{3} / k_{3}\right)\right) / k_{18}\\
\frac{dx_{2}}{dt} = \left(1 \cdot k_{18} \cdot k_{2} \cdot \left(1 - x_{3} / k_{3}\right) + -1 \cdot k_{18} \cdot k_{16} \cdot \left(1 - k_{17}\right) \cdot x_{4} \cdot x_{2}\right) / k_{18}\\
\frac{dx_{3}}{dt} = 1 \cdot k_{18} \cdot k_{2} \cdot \left(1 - x_{3} / k_{3}\right) / k_{18}\\
\frac{dx_{4}}{dt} = \left(1 \cdot k_{18} \cdot k_{4} \cdot x_{4} \cdot x_{1} + 1 \cdot k_{18} \cdot k_{16} \cdot \left(1 - k_{17}\right) \cdot x_{4} \cdot x_{2} + -1 \cdot k_{18} \cdot k_{5} \cdot x_{4}\right) / k_{18}\\
\frac{dx_{5}}{dt} = 1 \cdot k_{18} \cdot k_{5} \cdot x_{4} / k_{18}